EP2381248B1 - Système de mesure du débit de fluide avec correction pour la diffusion thermique - Google Patents

Système de mesure du débit de fluide avec correction pour la diffusion thermique Download PDF

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Publication number
EP2381248B1
EP2381248B1 EP11163139.6A EP11163139A EP2381248B1 EP 2381248 B1 EP2381248 B1 EP 2381248B1 EP 11163139 A EP11163139 A EP 11163139A EP 2381248 B1 EP2381248 B1 EP 2381248B1
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Prior art keywords
mixed gas
gas
temperature
heater element
measured
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German (de)
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EP2381248A1 (fr
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Yasuharu Ooishi
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Azbil Corp
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Azbil Corp
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/68—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by using thermal effects
    • G01F1/684—Structural arrangements; Mounting of elements, e.g. in relation to fluid flow
    • G01F1/6845—Micromachined devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/68—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by using thermal effects
    • G01F1/696—Circuits therefor, e.g. constant-current flow meters
    • G01F1/6965—Circuits therefor, e.g. constant-current flow meters comprising means to store calibration data for flow signal calculation or correction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F15/00—Details of, or accessories for, apparatus of groups G01F1/00 - G01F13/00 insofar as such details or appliances are not adapted to particular types of such apparatus
    • G01F15/02—Compensating or correcting for variations in pressure, density or temperature
    • G01F15/04—Compensating or correcting for variations in pressure, density or temperature of gases to be measured
    • G01F15/043—Compensating or correcting for variations in pressure, density or temperature of gases to be measured using electrical means
    • G01F15/046—Compensating or correcting for variations in pressure, density or temperature of gases to be measured using electrical means involving digital counting
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F25/00—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume
    • G01F25/10—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters
    • G01F25/15—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters specially adapted for gas meters

Definitions

  • the present invention relates to a thermal diffusivity measuring system, a concentration of caloric component measuring system, and a flow rate measuring system in relation to a gas inspection technology.
  • JP '138 Japanese Examined Patent Application Publication 2004-514138
  • JP '138 the method disclosed in JP '138 requires a costly speed-of-sound sensor to measure the speed of sound, in addition to a sensor for measuring the thermal conductivity. Because of this, measuring the amount of heat production by a mixed gas has not been easy.
  • the object of the present invention is to provide a thermal diffusivity measuring system, a concentration of caloric component measuring system, and a flow rate measuring system wherein the characteristics of a gas can be measured easily.
  • US 2005/0034532 A1 discloses a compensated flowmeter having a probe adapted to project into flowing media within a conduit.
  • the probe includes a thermal dispersion sensor, and a compensating gas properties sensor contained within a no-flow chamber of the probe.
  • FIG. 1 is a perspective diagram
  • FIG. 2 which is a cross-sectional diagram that is viewed from the direction of the section II-II.
  • the microchip 8A comprises a substrate 60A, which is provided with a cavity 66A, and a dielectric layer 65A, which is disposed so as to cover the cavity 66A on the substrate 60A.
  • the thickness of the substrate 60A is, for example, 0.5 mm.
  • the length and width dimensions of the substrate 60A are, for example, 1.5 mm each.
  • the portion of the dielectric layer 65A that covers the cavity 66A forms a thermally insulating diaphragm.
  • the microchip 8A further comprises a heater element 61A that is provided on a portion of the diaphragm of the dielectric layer 65A, a first temperature measuring element 62A and a second temperature measuring element 63A provided in a portion of the diaphragm of the dielectric layer 65A so that the heater element 61 A is interposed therebetween, and a third temperature measuring element 64A that is provided on the substrate 60A.
  • the heater element 61A is disposed in the center of the portion of the diaphragm of the dielectric layer 65A that covers the cavity 66A.
  • the heater element 61A is, for example, a resistor, and produces heat through the supply of electric power thereto, to heat the ambient gas that contacts the heater element 61A.
  • the first temperature measuring element 62A, the second temperature measuring element 63A, and the third temperature measuring element 64A are, for example, each resistors and each detect the gas temperature of the ambient gas prior to the production of heat by the heater element 61A. Note that the gas temperature may be measured using any single one of the first temperature measuring element 62A, the second temperature measuring element 63A, or the third temperature measuring element 64A.
  • an average value of the gas temperature detected by the first temperature measuring element 62A and the gas temperature detected by the second temperature measuring element 63A may be used as the gas temperature. While the description below is for an example wherein the average value of the gas temperatures detected by the first temperature measuring element 62A and the second temperature measuring element 63A is used as the gas temperature, there is no limitation thereto.
  • Silicon (Si), or the like, may be used as the material for the substrate 60A.
  • Silicon dioxide (SiO 2 ), or the like may be used as the material for the dielectric layer 65A.
  • the cavity 66A may be formed through anisotropic etching, or the like.
  • platinum (Pt) or the like may be used as the material for the first temperature measuring element 62A, the second temperature measuring element 63A, and the third temperature measuring element 64A, and they may be formed through a lithographic method, or the like.
  • one end of the heater element 61 A is connected electrically to a + input terminal of an operational amplifier 170, for example, with the other end grounded.
  • a resistive element 161 is connected, in parallel, to the + input terminal and the output terminal of the operational amplifier 170.
  • the - input terminal of the operational amplifier 170 is connected electrically between a resistive element 162 and a resistive element 163, which are connected in series, between the resistive element 163 and a resistive element 164, which are connected in series, between the resistive element 164 and a resistive element 165, which are connected in series, or between the resistive element 165 and a ground terminal.
  • the appropriate selection of the resistance values for each of the resistive elements 162 through 165 will produce a voltage V L3 of, for example, 2.4 V between the resistive element 163 and 162 when a voltage Vin of, for example, 5.0V is applied to one end of the resistive element 162. Additionally, a voltage V L2 of, for example, 1.9 V is produced between the resistive element 164 and the resistive element 163, and a voltage V L1 of, for example, 1.4 V is produced between the resistive element 165 and the resistive element 164.
  • a switch SW1 is connected between the resistive element 162 and the resistive element 163 and the - input terminal of the operational amplifier 170, and a switch SW2 is connected between the resistive element 163 and the resistive element 164 and the - input terminal of the operational amplifier 170. Furthermore, a switch SW3 is connected between the resistive element 164 and the resistive element 165 and the - input terminal of the operational amplifier 170, and a switch SW4 is connected between the resistive element 165 and ground terminal and the - input terminal of the operational amplifier 170.
  • any of three levels of voltages can be applied to the - input terminal of the operational amplifier 170 through turning the switches SW1, SW2, SW3, and SW4 ON and OFF. Because of this, the applied voltage that determines the heat producing temperature of the heater element 61 A can be set to any of three levels through turning the switches SW1, SW2, SW3, and SW4 ON and OFF.
  • Equation (1) R STD x 1 + ⁇ ⁇ T H - T STD + ⁇ ⁇ T H - T STD 2
  • T STD indicates a standard temperature of, for example, 20°C.
  • R STD indicates a resistance value that is measured in advance at the standard temperature of T STD .
  • a is the first-order temperature coefficient of resistance
  • ⁇ is the second-order temperature coefficient of resistance.
  • the heat producing temperature T H of the heater element 61A reaches a thermal equilibrium and stabilizes between the heater element 61A and the ambient gas.
  • thermal equilibrium refers to a state wherein there is a balance between the heat production by the heater element 61 A and the heat dissipation from the heater element 61 A into the ambient gas.
  • radiation coefficient M I of the ambient gas is obtained by dividing the driving power P H of the heater element 61A by the difference between the heat producing temperature T H of the heater element 61A and the temperature T I of the ambient gas in this equilibrium state.
  • the units for the radiation coefficient MI are, for example, W/°C.
  • M I P H / T H - T I
  • the heat producing temperature T H of the heater element 61 A can be calculated from Equation (1) through Equation (3), above.
  • the temperature T I of the ambient gas can be measured by the first temperature measuring element 62A and the second temperature measuring element 63A in FIG. 1 . Consequently, the radiation coefficient M I can be calculated using the microchip 8A illustrated in FIG. 1 and FIG. 2 .
  • Microchip 8A is secured, in a chamber, or the like, that is filled with the ambient gas, through, for example, a thermally insulating member that is disposed on the bottom face of the microchip 8A. Securing the microchip 8A through a thermally insulating member within a chamber, or the like, makes the temperature of the microchip 8A less susceptible to temperature variations of the inner wall of the chamber, or the like.
  • the thermally insulating member is made from glass, or the like, with a thermal conductivity of, for example, no more than 1.0 W/(m ⁇ K).
  • one end of the first temperature measuring element 62A is connected electrically to a - input terminal of an operational amplifier 270, for example, with the other end grounded.
  • a resistive element 261 is connected, in parallel, to the - input terminal and the output terminal of the operational amplifier 270.
  • the + input terminal of the operational amplifier 270 is connected electrically to between a resistive element 264 and a resistive element 265 that are connected in series. This causes a weak voltage of about 0.3 V to be applied to the first temperature measuring element 62A.
  • the temperature of the first temperature measuring element 62A, to which the weak voltage of about 0.3 V is applied, will approximate the ambient temperature T I .
  • the ambient gas is a mixed gas, where the mixed gas is assumed to comprise four gas components: gas A, gas B, gas C, and gas D.
  • gas A gas A
  • gas B gas B
  • gas C gas D
  • V A + V B + V C + V D 1
  • the radiation coefficient M I of the mixed gas is given by the sum of the products of the radiation coefficients of the individual gas components with the volume fractions of those gas components. Consequently, the radiation coefficient M I of the mixed gas is given by Equation (8), below.
  • M I M A x V A + M B x V B + M C x V C + M D x V D
  • Equation (10) the radiation coefficient M I (T H1 ) of the mixed gas, when the heat producing temperature of the heater element 61A is T H1 , is given by Equation (10), below.
  • the radiation coefficient M I (T H2 ) of the mixed gas, when the heat producing temperature of the heater element 61A is T H2 is given by Equation (11), below
  • the radiation coefficient M I (T H3 ) of the mixed gas, when the heat producing temperature of the heater element 61A is T H3 is given by Equation (12), below.
  • the heat producing temperature T H1 , the heat producing temperature T H2 , and the heat producing temperature T H3 are each different temperatures.
  • M I T H ⁇ 1 M A T H ⁇ 1 x V A + M B T H ⁇ 1 x V B + M C T H ⁇ 1 x V C + M D T H ⁇ 1 x V D
  • M I T H ⁇ 2 M A T H ⁇ 2 x V A + M B T H ⁇ 2 x V B + M C T H ⁇ 2 x V C + M D T H ⁇ 2 x V D
  • M I T H ⁇ 3 M A T H ⁇ 3 x V A + M B T H ⁇ 3 x V B + M C T H ⁇ 3 x V C + M D T H ⁇ 3 x V D
  • Equations (10) through (12) will have a linearly independent relationship if the rates of change of the radiation coefficients M A (T H ), M B (T H ), M C (T H ), and M D (T H ) of the individual gases with respect to the heat producing temperature T H of the heater element 61A are different. Moreover, if Equations (10) through (12) have a linearly independent relationship, then Equation (5) and Equations (10) through (12) will have a linearly independent relationship.
  • FIG. 5 is a graph illustrating the relationship between the heat producing temperature of the heater element 61A and the radiation coefficients of the methane ((CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ), which are included in natural gas.
  • the radiation coefficients of the respective gas components of the methane (CH4), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ), are linear with respect to the heat producing temperature of the heater element 61 A.
  • the rates of change of the radiation coefficients of the methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ), with respect to the heat producing temperature of the heater element 61 A are each different. Consequently, Equations (10) through (12), above, will be linearly independent if the gas components that comprise the mixed gas are methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ).
  • the values for the radiation coefficients M A (TH 1 ), M B (T H1 ), M C (T H1 ), M D (T H1 ), M A (T H2 ), M B (T H2 ), M C (T H2 ), M D (T H2 ), M A (T H3 ), M B (T H3 ), M C (T H3 ), and M D (T H3 ) for the individual gas components in Equations (10) through (12) can be obtained in advance through measurements, or the like.
  • the gas volume is proportional to the temperature of the gas itself by Boyle-Charles law. If, for example, the temperature of the mixed gas prior to the causing the heater element 61 A to produce heat is defined as T I , the volume fraction V A of the gas A, the volume fraction V B of the gas B, the volume fraction V C of the gas C, and the volume fraction V D of the gas D can be obtained as functions of the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas, and of the temperature T I of the mixed gas, as indicated in Equations (17) through (20), below.
  • V A f 1 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3
  • T I V B f 2 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3
  • T I V C f 3 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3
  • T I V D f 4 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3 , T I
  • Equation (21), below, is obtained through substituting Equation (17) through (20) into Equation (6), above.
  • the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured can be obtained uniquely by measuring the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas when the heat producing temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and then substituting into Equation (22). Note that if the temperature T I of the mixed gas previous to the heater element 61A being caused to produce heat is stable, then Equation (22) need not include the variable for the temperature T I of the mixed gas.
  • the gas components of the mixed gas are not limited to four different components.
  • the mixed gas comprises n types of gas components.
  • the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured is obtained uniquely by measuring the radiation coefficients M I (T H1 ), M I (T H2 ), M I (T H3 ), ..., M I (T Hn-1 ) of the mixed gas wherein the volume fractions of each of the n types of gas components is unknown when the heat producing temperatures of the heater element 61 A are n -1 different temperatures of T H1 , T H2 , T H3 , ..., T Hn-1 , and then substituting into Equation (23).
  • 1 / ⁇ g 1 ⁇ M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3 , ... , M 1 ⁇ T Hn - 1 , T I
  • the mixed gas includes an alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ), where j is a natural number, in addition to methane (CH 4 ) and propane (C 3 H 8 ), then the alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ) will be seen as a mixture of methane (CH 4 ) and propane (C 3 H 8 ), and there will be no effect on the calculation in Equation (23).
  • Equation (23) the calculation may be performed using Equation (23) by viewing ethane (C 2 H 6 ), butane (C 4 H 10 ), pentane (C 5 H 12 ), and hexane (C 6 H 14 ) as a mixture of methane (CH 4 ) and propane (C 3 H 8 ), with each multiplied by the respective specific factors.
  • a mixed gas comprising n types of gas components includes, as gas components, z types of alkanes (C j H 2j+2 ) other than methane ((CH 4 ) and propane (C 3 H 8 ), in addition to methane (CH4) and propane (C 3 H 8 ), an equation may be calculated having, as variables, the radiation coefficients M I of the mixed gas at, at least, n - z-1 different heat producing temperatures.
  • Equation (23) can be used in calculating the inverse 1/ ⁇ of the thermal diffusivity of gas to be measured.
  • Equation (23) can also be used when the mixed gas to be measured comprises a number of gas components that is less than n, where the gas components of the less than n different types are included in the mixed gas that was used for calculating Equation (3).
  • the mixed gas used in calculating Equation (23) included four types of gas components, namely methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ) and carbon dioxide (CO 2 ), then even if the mixed gas to be measured includes only three different components, namely methane (CH 4 ), propane (C 3 H 8 ), and carbon dioxide (CO 2 ), without containing the nitrogen (N 2 ), still Equation (23) can be used in calculating the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas to be measured.
  • Equation (23) could still be used even when the mixed gas being measured includes an alkane (C j H 2j+2 ) that was not included in the mixed gas that was used in calculating Equation (23). This is because, as described above, even if the alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ) is viewed as a mixture of methane (CH 4 ) and propane (C 3 H 8 ) there is no effect on calculating the inverse 1/ ⁇ of the thermal diffusivity using Equation (23).
  • the thermal diffusivity calculating equation generating system 20A having a chamber 101 that is filled with a sample mixed gas for which the inverse 1/ ⁇ of the thermal diffusivity is known; and a measuring mechanism 10, illustrated in FIG. 6 , for measuring the values of a plurality of radiation coefficients M I of the sample mixed gas and the temperature T I of the sample mixed gas, using the heater element 61A, the first temperature measuring element 62A, and the temperature measuring element 63A that are illustrated in FIG. 1 and FIG. 2 .
  • a gas physical property value measuring system includes a thermal diffusivity calculating equation generating portion 302 for generating a thermal diffusivity calculating equation using the radiation coefficients M I and the gas temperatures T I for a plurality of heat producing temperatures of the heater element 61 A as independent variables and the inverse 1/ ⁇ of the thermal diffusivity of the gas as the dependent variable, based on the values of the inverses 1/ ⁇ of known thermal diffusivities of a plurality of sample mixed gases, a plurality of measured values for the plurality of radiation coefficients M I of the sample mixed gases, and a plurality of measured values for the temperatures T I of the sample mixed gases.
  • the sample mixed gasses include a plurality of types of gases.
  • the measuring mechanism 10 comprises the microchip 8A that has been explained using FIG. 1 and FIG. 2 , disposed within the chamber 101, into which the sample mixed gasses are introduced.
  • the microchip 8A is disposed within the chamber 101, by means of a thermally insulating member 18.
  • a flow path 102, for feeding the sample mixed gasses into the chamber 101, and a flow path 103, for discharging the sample mixed gasses from the chamber 101, are connected to the chamber 101.
  • a first gas canister 50A for storing a first sample mixed gas a first gas canister 50A for storing a first sample mixed gas
  • a second gas canister 50B for storing a second sample mixed gas a third gas canister 50C for storing a third sample mixed gas
  • a fourth gas canister 50D for storing a fourth sample mixed gas are prepared.
  • the first gas canister 50A is connected, through a flow path 91A to a first gas pressure regulating device 31A for providing the first sample mixed gas from the first gas canister 50A, regulated to a low-pressure such as, for example, 0.2 MPa.
  • a first flow rate controlling device 32A is connected through a flow path 92A to the first gas pressure regulating device 31A.
  • the first flow rate controlling device 32A controls the rate of flow of the first sample mixed gas that is fed into the thermal diffusivity calculating equation generating system 20A through the flow path 92A and the flow path 102.
  • a second flow gas pressure regulating device 31 B is connected through a flow path 91B to the second gas canister 50B. Additionally, a second flow rate controlling device 32B is connected through a flow path 92B to the second gas pressure regulating device 31 B. The second flow rate controlling device 32B controls the rate of flow of the second sample mixed gas that is fed into the thermal diffusivity calculating equation generating system 20A through the flow paths 92B, 93, and 102.
  • a third flow gas pressure regulating device 31C is connected through a flow path 91C to the third gas canister 50C. Additionally, a third flow rate controlling device 32C is connected through a flow path 92C to the third gas pressure regulating device 31C. The third flow rate controlling device 32C controls the rate of flow of the third sample mixed gas that is fed into the thermal diffusivity calculating equation generating system 20A through the flow paths 92C, 93, and 102.
  • the first through fourth at sample mixed gases are each, for example, natural gas.
  • the first through fourth sample mixed gases each include four different gas components of, for example, methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ).
  • the first temperature measuring element 62A and the second temperature measuring element 63A, illustrated in FIG. 1 and FIG. 2 , of the microchip 8A detect the temperature T I of the first sample mixed gas prior to the production of heat by the heater element 61 A. Thereafter, the heater element 61 A applies a driving power P H from the driving circuit 303 illustrated in FIG. 6 .
  • the application of the driving power P H causes the heater element 61 A, illustrated in FIG. 1 and FIG. 2 , to produce heat at, for example, 100°C, 150°C, and 200°C.
  • the second through fourth sample mixed gases are filled sequentially into the chamber 101.
  • the microchip 8A detects the respective temperatures of the second through fourth sample mixed gases.
  • the heater element 61A illustrated in FIG. 1 and FIG. 2 , to which the driving power P H is applied, produces heat at 100°C, 150°C, and 200°C.
  • the heater element 61A illustrated in FIG. 1 and FIG. 2 , is caused to reduce heat at at least n-1 different heat producing temperatures.
  • alkane (C j H 2j+2 ) other than methane (CH4) and propane (C 3 H 8 ) can be viewed as a mixture of methane (CH 4 ) and propane (C 3 H 8 ).
  • a sample mixed gas comprising n types of gas components includes, as gas components, z types of alkanes (C j H 2j+2 ) in addition to methane (CH 4 ) and propane (C 3 H 8 ), the heater element 61A is caused to produce heat at n-z-1 different heat producing temperatures.
  • the measuring mechanism 10 illustrated in FIG. 6 is provided with a central calculation processing device (CPU) 300 that includes a radiation coefficient calculating portion 301 that is connected to the microchip 8A.
  • the radiation coefficient calculating portion 301 divides a first driving power P H1 of the heater element 61A of the microchip 8A that is illustrated in FIG. 1 and FIG. 2 by the difference between a first heat producing temperature T H of the heater element 61 A (for example, 100°C) and the temperature T I for each of the first through fourth sample mixed gases. Doing so calculates the value for the radiation coefficient M I for each of the first through fourth sample mixed gases in thermal equilibrium with the heater element 61 A with the heat producing temperature of 100°C.
  • the radiation coefficient calculating portion 301 illustrated in FIG. 6 divides a second driving power P H2 of the heater element 61 A of the microchip 8A that is illustrated in FIG. 1 and FIG. 2 by the difference between a second heat producing temperature T H of the heater element 61 A (for example, 150°C) and the temperature T I for each of the first through fourth sample mixed gases. Doing so calculates the value for the radiation coefficient M I for each of the first through fourth sample mixed gases in thermal equilibrium with the heater element 61A with the heat producing temperature of 150°C.
  • a second heat producing temperature T H of the heater element 61 A for example, 150°C
  • the radiation coefficient calculating portion 301 illustrated in FIG. 6 divides a third driving power P H3 of the heater element 61A of the microchip 8A that is illustrated in FIG. 1 and FIG. 2 by the difference between a third heat producing temperature T H of the heater element 61A (for example, 200°C) and the temperature T I for each of the first through fourth sample mixed gases. Doing so calculates the value for the radiation coefficient M I for each of the first through fourth sample mixed gases in thermal equilibrium with the heater element 61A with the heat producing temperature of 200°C.
  • a third heat producing temperature T H of the heater element 61A for example, 200°C
  • the thermal diffusivity calculating equation generating system 20 illustrated in FIG. 6 is further provided with a radiation coefficient storing device 401, connected to the CPU 300.
  • the radiation coefficient calculating portion 301 stores, in the radiation coefficient storing device 401, the measured gas temperature values T I and the calculated values for the radiation coefficients M I .
  • the thermal diffusivity calculating equation generating portion 302 collects the respective known inverse 1/ ⁇ values for the thermal diffusivities for the first through fourth sample mixed gases, for example, the plurality of measured values for the radiation coefficients M I for when the heat producing temperature of the heater element 61A was 100°C, the plurality of measured values for the radiation coefficients M I for when the heat producing temperature of the heater element 61 A was 150°C, and the plurality of measured values for the radiation coefficients M I for when the heat producing temperature of the heater element 61 A was 200°C.
  • the thermal diffusivity calculating equation generating portion 302 calculates a thermal diffusivity calculating equation having, as independent variables, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 100°C, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 150°C, the radiation coefficient M I when the heat producing temperature of the heater element 61 A is 200°C, and the gas temperature T I , and having, as the dependent variable, the inverse 1/ ⁇ of the thermal diffusivity.
  • multivariate analysis includes support vector analysis disclosed in A. J. Smola and B. Scholkopf (eds.), “A tutorial on Support Vector Regression” (NeuroCOLT Technical Report NC-TR-98-030 ), multiple linear regression analysis, the Fuzzy Quantification Theory Type II, disclosed in Japanese Unexamined Patent Application Publication H5-141999 , and the like. Additionally, the radiation coefficient calculating portion 301 and the thermal diffusivity calculating equation generating portion 302 are included in the CPU 300.
  • the thermal diffusivity calculating equation generating system 20A is further provided with a thermal diffusivity calculating equation storing device 402, connected to the CPU 300.
  • the thermal diffusivity calculating equation storing device 402 stores the thermal diffusivity calculating equation generated by the thermal diffusivity calculating equation generating portion 302.
  • An inputting device 312 and an outputting device 313 are also connected to the CPU 300.
  • a keyboard, a pointing device such as a mouse, or the like, may be used as the inputting device 312.
  • An image displaying device such as a liquid crystal display or a monitor, or a printer, or the like, may be used as the outputting device 313.
  • FIG. 8 The flowchart in FIG. 8 will be used next to explain a method for generating a thermal diffusivity calculating equation. Note that in the example below a case will be explained wherein the first through fourth sample mixed gases are prepared and the heater element 61 A of the microchip 8A illustrated in FIG. 6 is caused to produce heat at 100°C, 150°C, and 200°C.
  • the method for generating a thermal diffusivity calculating equation as set forth enables the generation of a thermal diffusivity calculating equation that calculates a unique value for the thermal diffusivity ⁇ of a mixed gas being measured.
  • a thermal diffusivity measuring system 21A includes a chamber 101 that is filled with a mixed gas to be measured for which the inverse 1/ ⁇ of the thermal diffusivity is unknown; and a measuring mechanism 10, illustrated in FIG. 9 , for measuring the values of a plurality of radiation coefficients M I of the mixed gas being measured and the temperature TI of the mixed gas being measured, using the heater element 61 A, the first temperature measuring element 62A, and the second temperature measuring element 63A that are illustrated in FIG. 1 and FIG. 2 .
  • the thermal diffusivity measuring system 21A further has a thermal diffusivity calculating equation storing device 402 for storing a thermal diffusivity calculating equation having, as independent variables, the temperature T I of the gas and the radiation coefficients M I for the gas at a plurality of heat producing temperatures of the heater element 61 A, and having, as the independent variable, the inverse 1/ ⁇ of the thermal diffusivity; and a thermal diffusivity calculating portion 305 for calculating the value of the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured, by substituting the value for the temperature T I of the mixed gas being measured and the radiation coefficients M I , for the mixed gas being measured, at a plurality of heat producing temperatures of the heater element 61 A into the independent variables of the temperature T I of the gas and the radiation coefficients M I for the gas at a plurality of heat producing temperatures of the heater element 61 A in the thermal diffusivity calculating equation.
  • the thermal diffusivity calculating equation storing device 402 stores the thermal diffusivity calculating equation.
  • natural gases including methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ) were used as the sample mixed gases for generating the thermal diffusivity calculating equation.
  • the thermal diffusivity calculating equation uses, as independent variables, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 100°C, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61 A is 150°C, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 200°C, and the temperature T I of the gas.
  • a natural gas that includes, in unknown volume fractions, methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ) and for which the inverse 1/ ⁇ of the thermal diffusivity is unknown, is introduced into the chamber 101 as the mixed gas to be measured.
  • the first temperature measuring element 62A and the second temperature measuring element 63A, illustrated in FIG. 1 and FIG. 2 , of the microchip 8A detect the temperature T I of the mixed gas to be measured, prior to the production of heat by the heater element 61A. Thereafter, the heater element 61A applies a driving power P H from the driving circuit 303 illustrated in FIG. 9 .
  • the application of the driving power P H causes the heater element 61A, illustrated in FIG. 1 and FIG. 2 , to produce heat at 100°C, 150°C, and 200°C.
  • the radiation coefficient calculating portion 301 follows the method explained by Equations (1) to (4), above, to calculate the value of the radiation coefficient M I of the mixed gas being measured when at thermal equilibrium with the heater element 61A producing heat at the heat producing temperature of 100°C. Moreover, the radiation coefficient calculating portion 301 calculates the value of the radiation coefficient M I of the mixed gas being measured when at thermal equilibrium with the heater element 61A producing heat at the heat producing temperature of 150°C and the value of the radiation coefficient M I of the mixed gas being measured when at thermal equilibrium with the heater element 61A producing heat at the heat producing temperature of 200°C. The radiation coefficient calculating portion 301 stores, in the radiation coefficient storing device 401, the gas temperature value T I of the mixed gas being measured and the calculated values for the radiation coefficients M I .
  • the thermal diffusivity calculating portion 305 substitutes the values of the radiation coefficients M I and the temperature T I of the mixed gas being measured into the independent variables of the radiation coefficients M I for the gas and the temperature T I of the gas in the thermal diffusivity calculating equation, to calculate the value of the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured.
  • the thermal diffusivity calculating portion 305 may further calculate the value of the thermal diffusivity ⁇ from the value of the inverse 1/ ⁇ of the thermal diffusivity.
  • a thermal diffusivity storing device 403 is also connected to the CPU 300.
  • the thermal diffusivity storing device 403 stores the value of the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured, calculated by the thermal diffusivity calculating portion 305.
  • the requirements for the other structural elements in the thermal diffusivity measuring system 21 A as set forth here are identical to those in the thermal diffusivity calculating equation generating system 20A set forth above, so explanations thereof are omitted.
  • the flowchart in FIG. 10 will be used next to explain a method for measuring a thermal diffusivity. Note that in the example below a case will be explained the heater element 61A of the microchip 8A illustrated in FIG. 9 is caused to produce heat at 100°C, 150°C, and 200°C.
  • the method for measuring the thermal diffusivity as set forth in the example described above enables the measurement of the thermal diffusivity ⁇ of a mixed gas that is a mixed gas to be measured, from measured values for the radiation coefficients M I of the mixed gas to be measured, without using costly gas chromatography equipment or speed-of-sound sensors.
  • the equation for calculating the inverse 1/ ⁇ of the thermal diffusivity was used to calculate calculated values for the inverses 1l ⁇ of the thermal diffusivities for the 19 sample mixed gases, and the true values for the inverses 1/ ⁇ of the thermal diffusivities for the 19 sample mixed gases were compared.
  • T H 1 / 2 ⁇ ⁇ x - ⁇ + ⁇ 2 - 4 ⁇ ⁇ ⁇ 1 - R H / R H_STD 1 / 2 + T H_STD
  • the temperature of the first temperature measuring element 62A when power is applied to the extent that it does not produce heat itself, will approximate the ambient temperature T I .
  • T I_STD indicates a standard temperature for the first temperature measuring element 62A of, for example, 20°C.
  • R I_STD indicates a resistance value that is measured in advance for the first temperature measuring element 62A at the standard temperature of T I-STD .
  • T I 1 / 2 ⁇ ⁇ x - ⁇ + ⁇ 2 - 4 ⁇ ⁇ I ⁇ 1 - R I / R I_STD 1 / 2 + T I_STD
  • M I P H / ⁇ ⁇ T H P H / [ 1 / 2 ⁇ ⁇ x - ⁇ + ⁇ 2 - 4 ⁇ ⁇ ⁇ 1 - R H / R H_STD 1 / 2 + T H_STD - 1 / 2 ⁇ ⁇ ⁇ - ⁇ + ⁇ 2 - 4 ⁇ ⁇ ⁇ 1 - R I / R I_STD 1 / 2 - T I_STD
  • the resistance R H of the heater element 61A can be calculated from Equation (2) through Equation (3), above. Similarly, it is also possible to calculate the resistance value R I of the first temperature measuring element 62A.
  • the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas that comprises the four types of gas components is obtained from an equation having, as variables, the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas when the heat producing temperatures of the heater element 61A are T H1, T H2 , and T H3 .
  • the radiation coefficient M I of the mixed gas depends on the resistance value R H of the heater element 61A and on the resistance value R I of the first temperature measuring element 62A.
  • the inventors discovered that the inverse 1/ ⁇ of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the resistances R H1 (T H1 ), R H2 (T H2 ), and R H3 (T H3 ) of the heater element 61 A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the resistance value R I of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (33), below.
  • 1 / ⁇ g 2 R H ⁇ 1 T H ⁇ 1 , R H ⁇ 2 T H ⁇ 2 , R H ⁇ 3 T H ⁇ 3 , R I
  • the inverse 1/ ⁇ of the thermal diffusivity of a mixed gas can be calculated uniquely by measuring the resistances R H1 (T H1 ), R H2 (T H2 ), and R H3 (T H3 ) of the heater element 61 A when the heat producing temperatures of the heater element 61 A, which is in contact with the mixed gas, are T H1 , T H2 , and T H3 , and the resistance value R I of the first temperature measuring element 62A that is in contact with the mixed gas prior to the heat production by the heater element 61A, for example, and then substituting into Equation (33).
  • the inverse 1/ ⁇ of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the currents I H1 (T H1 ), I H2 (T H2 ), and I H3 (T H3 ) flowing in the heater element 61A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the current I I flowing in the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (34), below.
  • 1 / ⁇ g 3 I H ⁇ 1 T H ⁇ 1 , I H ⁇ 2 T H ⁇ 2 , I H ⁇ 3 T H ⁇ 3 , I I I
  • the inverse 1/ ⁇ of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the voltages V H1 (T H1 ), V H2 (T H2 ), and V H3 (T H3 ) of the heater element 61 A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the voltage V I of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (35), below.
  • 1 / ⁇ g 4 V H ⁇ 1 T H ⁇ 1 , V H ⁇ 2 T H ⁇ 2 , V H ⁇ 3 T H ⁇ 3 , V I
  • the inverse 1/ ⁇ of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the output voltages AD H1 (T H1 ), AD H2 (T H2 ), and AD H3 (T H3 ) of analog-digital converting circuits (hereinafter termed "A/D converting circuits") that are connected to the heater element 61A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the output voltage AD I of an A/D converting circuit that is connected to the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (36), below.
  • 1 / ⁇ g 5 AD H ⁇ 1 T H ⁇ 1 , AD H ⁇ 2 T H ⁇ 2 , AD H ⁇ 3 T H ⁇ 3 , AD I
  • the inverse 1/ ⁇ of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61 A when the heat producing temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and an electric signal S I from the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (37), below.
  • 1 / ⁇ g 6 S H ⁇ 1 T H ⁇ 1 , S H ⁇ 2 T H ⁇ 2 , S H ⁇ 3 T H ⁇ 3 , S I
  • a thermal diffusivity calculating equation generating system 20B as illustrated in FIG. 14 includes a measuring portion 321, illustrated in FIG. 14 , for measuring values of electric signals S I from the first temperature measuring element 62A, illustrated in FIG. 1 and FIG. 2 , that are dependent on the respective temperatures T I of the plurality of sample mixed gases, and the values of electric signals S H from the heater element 61A at each of the plurality of heat producing temperatures T H ; and a thermal diffusivity calculating equation generating portion 302 for generating a thermal diffusivity calculating equation based on known values for inverses 1/ ⁇ of thermal diffusivities of a plurality of sample mixed gases, the plurality of measured values for the electric signals S I from the first temperature measuring element 62A, and the plurality of measured values for the electric signals from the heater element 61 A at the plurality of heat producing temperatures, having an electric signal S I from the first temperature measuring element 62A and the electric signals S H from the heater element 61 A at the plurality of heat producing temperatures T H as independent
  • the first temperature measuring element 62A of the microchip 8A After a first sample mixed gas is filled into the chamber 101, the first temperature measuring element 62A of the microchip 8A, illustrated in FIG. 1 and FIG. 2 , outputs an electric signal S I that is dependent on the temperature of the first sample mixed gas.
  • the heater element 61 A applies driving powers P H1 , P H2 , and P H3 from the driving circuit 303 illustrated in FIG. 14 .
  • the heater element 61A that is in contact with the first sample mixed gas produces heat at a temperature T H1 of 100°C, a temperature T H2 of 150°C, and a temperature T H3 of 200°C, for example, to output an electric signal S H1 (T H1 ) at the heat producing temperature T H1 , an electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and an electric signal S H3 (T H3 ) at the heat producing temperature T H3 .
  • the second through fourth sample mixed gases are filled sequentially into the chamber 101.
  • the first temperature measuring element 62A of the microchip 8A illustrated in FIG. 1 and FIG. 2 , outputs an electric signal S I that is dependent on the temperature of the second sample mixed gas.
  • the heater element 61A which is in contact with the second sample mixed gas, outputs an electric signal S H1 (T H1 ) at a heat producing temperature T H1, an electric signal S H2 (T H2 ) at a heat producing temperature T H2 , and an electric signal S H3 (T H3 ) at a heat producing temperature T H3 .
  • the first temperature measuring element 62A of the microchip 8A outputs an electric signal S I that is dependent on the temperature of the third sample mixed gas.
  • the heater element 61A which is in contact with the third sample mixed gas, outputs an electric signal S H1 (T H1 ) at a heat producing temperature T H1 , an electric signal S H2 (T H2 ) at a heat producing temperature T H2 , and an electric signal S H3 (T H3 ) at a heat producing temperature T H3 .
  • the first temperature measuring element 62A of the microchip 8A outputs an electric signal S I that is dependent on the temperature of the fourth sample mixed gas.
  • the heater element 61A which is in contact with the fourth sample mixed gas, outputs an electric signal S H1 (T H1 ) at a heat producing temperature T H1 , an electric signal S H2 (T H2 ) at a heat producing temperature T H2 , and an electric signal S H3 (T H3 ) at a heat producing temperature T H3 .
  • the heater element 61A illustrated in FIG. 1 and FIG. 2 , is caused to reduce heat at at least n-1 different temperatures.
  • alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ) can be viewed as a mixture of methane (CH 4 ) and propane (C 3 H 8 ).
  • a sample mixed gas comprising n types of gas components includes, as gas components, z types of alkanes (C j H 2j+2 ) in addition to methane (CH 4 ) and propane (C 3 H 8 ), the heater element 61A is caused to produce heat at n-z-1 different temperatures.
  • the microchip 8A is connected to a CPU that includes the measuring portion 321.
  • An electric signal storing device 421 is also connected to the CPU 300.
  • the measuring portion 321 measures the value of the electric signal S I from the first temperature measuring element 62A, and, from the heater element 61 A, the values of the electric signal S H1 (T H1 ) at the heat producing temperature T H1 , the electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and the electric signal S H3 (T H3 ) at the heat producing temperature T H3 , and stores the measured values in the electric signal storing device 421.
  • the electric signal S I from the first temperature measuring element 62A may be the resistance value R I of the first temperature measuring element 62A, the current I I flowing in the first temperature measuring element 62A, the voltage V I applied to the first temperature measuring element 62A, or the output signal AD I from the A/D converting circuit 304 that is connected to the first temperature measuring element 62A.
  • the electric signal SH from the heater element 61A may be the resistance value R H of the heater element 61 A, the current I H flowing in the heater element 61 A, the voltage V H applied to the heater element 61A, or the output signal AD H from the A/D converting circuit 304 that is connected to the heater element 61A.
  • the thermal diffusivity calculating equation generating portion 302 that is included in the CPU 300 collection the respective known values for the inverses 1/ ⁇ of the thermal diffusivities for, for example, each of the first through fourth sample mixed gases, the plurality of measured values for the electric signals S 1 from the first temperature measuring element 62A, and the plurality of measured values for the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61A.
  • the thermal diffusivity calculating equation generating portion 302 uses multivariate analysis based on the collected values for the inverses 1/ ⁇ of the thermal diffusivities, the electric signals S 1 , and the electric signals S H , to generate a thermal diffusivity calculating equation having the electric signal S I from the first temperature measuring element 62A and the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61A as the independent variables, and the inverse 1/ ⁇ of the thermal diffusivity as the dependent variable.
  • the other structural elements of the thermal diffusivity calculating equation generating system 20B illustrated in FIG. 14 are identical to those of the thermal diffusivity calculating equation generating system 20A that is illustrated in FIG. 6 , so explanations thereof are omitted.
  • a thermal diffusivity measuring system 21 B as set forth has a measuring portion 321 for measuring the value of an electric signal S I from the first temperature measuring element 62A, which is dependent on the temperature T I of the gas being measured, and values of the electric signals S H from the heater element 61 A at each of the plurality of heat producing temperatures T H ; a thermal diffusivity calculating equation storing device 402 for storing a thermal diffusivity calculating equation that has the electric signal S I from the first temperature measuring element 62A and the electric signals S H from the heater element 61A at the plurality of heat producing temperatures T H as independent variables and the inverse 1/ ⁇ of the thermal diffusivity as the dependent variable; and a thermal diffusivity calculating portion 305 for calculating the value of the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured, by substituting the measured value of the electric signal S I from the first temperature measuring element 62A and the measured values of the electric signals S H from the heater element 61 A into the independent
  • the thermal diffusivity calculating equation includes, for example, as independent variables, the electric signal S I from the first temperature measuring element 62A, the electric signal S H1 (T H1 ) from the heater element 61A at a heat producing temperature T H1 of 100°C, the electric signal S H2 (T H2 ) from the heater element 61A at a heat producing temperature T H2 of 150°C, and the electric signal S H3 (T H3 ) from the heater element 61A at a heat producing temperature T H3 of 200°C.
  • the first temperature measuring element 62A of the microchip 8A illustrated in FIG. 1 and FIG. 2 outputs an electric signal S I that is dependent on the temperature of the gas that is measured.
  • the heater element 61A applies driving powers P H1 , P H2 , and P H3 , from the driving circuit 303 illustrated in FIG. 15 .
  • the driving powers P H1 , P H2, and P H3 are applied, the heater element 61A that is in contact with the mixed gas being measured produces heat at a temperature T H1 of 100°C, a temperature T H2 of 150°C, and a temperature T H3 .
  • the measuring portion 32 measures the value of the electric signal S I from the first temperature measuring element 62A, which is in contact with the mixed gas being measured, and, from the heater element 61A, which is in contact with the mixed gas being measured, the values of the electric signal S H1 (T H1 ) at the heat producing temperature T H1 , the electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and the electric signal S H3 (T H3 ) at the heat producing temperature T H3 , and stores the measured values in the electric signal storing device 421.
  • the thermal diffusivity calculating portion 305 substitutes the respected respective measured values into the independent variables of the electric signal S I from the first temperature measuring element 62A and the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61A in the thermal diffusivity calculating equation that is stored in the thermal diffusivity calculating equation storing device 402, to calculate the value of the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas.
  • the other structural elements of the thermal diffusivity measuring system 21 B illustrated in FIG. 15 are identical to those of the thermal diffusivity measuring system 21 A that is illustrated in FIG. 9 , so explanations thereof are omitted.
  • the natural gas includes caloric components such as methane (CH 4 ) and propane (C 3 H 8 ), and non-caloric components such as nitrogen (N 2 ) and carbon dioxide (CO 2 ).
  • caloric components such as methane (CH 4 ) and propane (C 3 H 8 )
  • non-caloric components such as nitrogen (N 2 ) and carbon dioxide (CO 2 ).
  • concentration of caloric component C 0 of the caloric components such as alkanes (C n H 2n+2 ) in the mixed gas and the radiation coefficient of the mixed gas will be explained next.
  • Equation (39), below, is obtained through substituting Equations (17) through (20), above, into Equation (38), above.
  • the unit-volume calorific value Q of the mixed gas is obtained from an equation having, as variables, the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas, and the temperature T I of the mixed gas, when the heat producing temperatures of the heater element 61 A are T H1 , T H2 , and T H3 . Consequently, the calorific value Q of the mixed gas is given by Equation (40), below, where h 1 is a code indicating a function.
  • Q h 1 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3 , T I
  • the calorific value Q of the mixed gas being measured can be obtained uniquely by measuring the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas when the heat producing temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and then substituting into Equation (40).
  • the calorific value Q of the mixed gas is proportional to the concentration of caloric component Co of the alkanes, and the like, in the mixed gas. Consequently, the concentration of caloric component Co in the mixed gas is given by Equation (41), below, where h 2 is a code indicating a function.
  • C 0 h 2 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3 , T I
  • Equation (42) the concentration of caloric component C 0 in the mixed gas is given by Equation (42), below.
  • C 0 h 2 ⁇ M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3 , ... , M I ⁇ T Hn - 1 , T I
  • Equation (42) if the mixed gas includes an alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ), where j is a natural number, in addition to methane (CH 4 ) and propane (C 3 H 8 ), then the alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ) will be seen as a mixture of methane (CH 4 ) and propane (C 3 H 8 ), so there will be no effect on the calculation in Equation (42). Also, if the temperature T I of the mixed gas previous to the heater element 61 A, illustrated in FIG. 1 and FIG. 2 , being caused to produce heat is stable, then Equation (42) need not include the variable for the temperature T I of the mixed gas.
  • the concentration of caloric component calculating equation generating system 22A includes a chamber 101 that is filled with sample mixed gases for which the caloric component densities Co are known in advance, and a measuring mechanism 10 for measuring the values of a plurality of radiation coefficients M I of the sample mixed gases and the values of the temperatures T I of the sample mixed gases.
  • the concentration of caloric component calculating equation generating system 22A has a density calculating equation generating portion 352 for generating a concentration of caloric component calculating equation using the radiation coefficients M I and the gas temperatures T I for a plurality of heat producing temperatures of the heater element 61 A as independent variables and the concentration of caloric component C 0 of the gas as the dependent variable, based on the values of the caloric component densities C 0 of a plurality of sample mixed gases, a plurality of measured values for the plurality of radiation coefficients M I of the sample mixed gases, and a plurality of measured values for the temperatures T I of the sample mixed gases.
  • the measuring mechanism 10 and heat dissipation factor storing device 401 are the same as in the above examples, so the explanations thereof are omitted.
  • the density calculating equation generating portion 352 collects the respective known caloric component densities C 0 of the first through fourth sample mixed gases, for example, the plurality of measured values for the radiation coefficients M I for the gas when the heat producing temperature of the heater element 61 A was 100°C, the plurality of measured values for the radiation coefficients M I for the gas when the heat producing temperature of the heater element 61A was 150°C, and the plurality of measured values for the gas the radiation coefficients M I for when the heat producing temperature of the heater element 61A was 200°C.
  • the density calculating equation generating portion 352 calculates a concentration of caloric component calculating equation having, as independent variables, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 100°C, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 150°C, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 200°C, and the gas temperature T I , and having, as the dependent variable, the concentration of caloric component C 0 .
  • the concentration of caloric component calculating equation generating system 22A is further provided with a density calculating equation storing device 452, connected to the CPU 300.
  • the density calculating equation storing device 452 stores the concentration of caloric component calculating equation generated by the density calculating equation generating portion 352.
  • the flowchart in FIG. 17 is used next to explain a method for generating a concentration of caloric component calculating equation. Note that in the example below a case is explained wherein the first through fourth sample mixed gases are prepared and the heater element 61 A of the microchip 8A illustrated in FIG. 16 is caused to produce heat at 100°C, 150°C, and 200°C.
  • the method for generating a concentration of caloric component calculating equation as set forth enables the generation of a concentration of caloric component calculating equation that calculates a unique value for the concentration of caloric component C 0 of a mixed gas being measured.
  • a concentration of caloric component measuring system 23A according to a further example illustrated in FIG. 18 has a chamber 101 that is filled with a mixed gas to be measured for which the concentration of caloric component C 0 is unknown, and a measuring mechanism 10 for measuring the value of the temperature T I of the mixed gas to be measured and the values of a plurality of radiation coefficients M I of the mixed gas to be measured.
  • the concentration of caloric component measuring system 23A further has a density calculating equation storing device 452 for storing a concentration of caloric component calculating equation having, as independent variables, the temperature T I of the gas and the radiation coefficients M I for the gas at a plurality of heat producing temperatures of the heater element 61 A, and having, as the independent variable, the concentration of caloric component Co; and a density calculating portion 355 for calculating the value of the concentration of caloric component C 0 of the mixed gas being measured, by substituting the value for the temperature T I of the mixed gas being measured and the radiation coefficients M I , for the mixed gas being measured, at a plurality of heat producing temperatures of the heater element 61A into the independent variables of the temperature T I of the gas and the radiation coefficients M I for the gas at a plurality of heat producing temperatures of the heater element 61A in the thermal diffusivity calculating equation.
  • the density calculating equation storing device 452 stores the concentration of caloric component calculating equation as described above.
  • natural gases including methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ), were used as the sample mixed gases for generating the concentration of caloric component calculating equation.
  • the concentration of caloric component calculating equation uses, as independent variables, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 100°C, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 150°C, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 200°C, and the temperature T I of the gas.
  • a natural gas that includes, in unknown volume fractions, methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ), and for which the concentration of caloric component C 0 is unknown, is introduced into the chamber 101 as the mixed gas to be measured.
  • the measuring mechanism 10 and heat dissipation factor storing device 401 are the same as above, so the explanations thereof are omitted.
  • the density calculating portion 355 substitutes the values of the radiation coefficients M I and the temperature T I of the mixed gas being measured into the independent variables of the radiation coefficients M I for the gas and the temperature T I of the gas in the concentration of caloric component calculating equation, to calculate the value of the concentration of caloric component C 0 of the mixed gas being measured.
  • a density storing device 453 is also connected to the CPU 300. The density storing device 453 stores the value of concentration of caloric component C 0 of the mixed gas being measured, calculated by the density calculating portion 355.
  • the requirements for the other structural elements in the concentration of caloric component measuring system 23A as set forth therein are identical to those in the concentration of caloric component calculating equation generating system 22A set forth above, so explanations thereof are omitted.
  • the flowchart in FIG. 19 is used next to explain a method for measuring a concentration of caloric component. Note that in the example below a case is explained the heater element 61A of the microchip 8A illustrated in FIG. 18 is caused to produce heat at 100°C, 150°C, and 200°C.
  • the method for measuring the concentration of caloric component as described above enables the measurement of the concentration of caloric component C 0 in a mixed gas that is a mixed gas to be measured, from measured values for the radiation coefficients M I of the mixed gas to be measured, without using costly gas chromatography equipment or speed-of-sound sensors.
  • 19 different sample mixed gases having mutually differing volume densities of ethane, propane, butane, nitrogen, and carbon dioxide, were prepared.
  • the values of the radiation coefficient M I for each of the 19 mixed gas samples are measured when the heater element has been caused to produce heat at a plurality of temperatures.
  • support vector regression based on the known values for the alkane densities C 0 of the 19 sample mixed gases and the plurality of measured values for the radiation coefficients M I , was used to generate an equation for calculating the alkane density C 0 using the radiation coefficients M I as independent variables and the alkane density C 0 as the dependent variable.
  • the equation for calculating the alkane density C 0 was used to calculate calculated values for the alkane densities C 0 for the 19 sample mixed gases, and the true values for the alkane densities C 0 for the 19 sample mixed gases were compared.
  • the error in the calculated values relative to the true values for the alkane densities C 0 , as illustrated in FIG. 21 and FIG. 22 , where within -0.3% and +0.3%.
  • the ability to calculate accurately alkane density C 0 from measured values for radiation coefficients M I through the use of an alkane density C 0 calculating equation that has the radiation coefficients M I as the independent variables and the alkane density C 0 as the dependent variable was thus demonstrated.
  • the concentration of caloric component C 0 of the mixed gas that comprises the four types of gas components is obtained as an equation having, as variables, the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas when the heat producing temperatures of the heater element 61A are T H1 , T H2 , and T H3 .
  • the radiation coefficient M I of the mixed gas depends on the resistance value R H of the heater element 61A and on the resistance value R I of the first temperature measuring element 62A.
  • the concentration of caloric component C 0 of a mixed gas can also be obtained as an equation having, as variables, the resistances R H1 (T H1 ), R H2 (T H2 ), and R H3 (T H3 ) of the heater element 61A when the temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and the resistance value R I of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (43), below.
  • C 0 h 3 R H ⁇ 1 T H ⁇ 1 , R H ⁇ 2 T H ⁇ 2 , R H ⁇ 3 T H ⁇ 3 , R I
  • the concentration of caloric component C 0 of a mixed gas can be calculated uniquely by measuring the resistances R H1 (T H1 ), R H2 (T H2 ), and R H3 (T H3 ) of the heater element 61A when the heat producing temperatures of the heater element 61A, which is in contact with the mixed gas, are T H1 , T H2 , and T H3 , and the resistance value R I of the first temperature measuring element 62A that is in contact with the mixed gas prior to the heat production by the heater element 61A, for example, and then substituting into Equation (43).
  • the concentration of caloric component C 0 of a mixed gas can also be obtained as an equation having, as variables, the currents I H1 (T H1 ), I H2 (T H2 ), and I H3 (T H3 ) flowing in the heater element 61 A when the temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and the current I I flowing in the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (44), below.
  • C 0 h 4 I H ⁇ 1 T H ⁇ 1 , I H ⁇ 2 T H ⁇ 2 , I H ⁇ 3 T H ⁇ 3 , I I I
  • the concentration of caloric component C 0 of a mixed gas can also be obtained from an equation having, as variables, the voltages V H1 (T H1 ), V H2 (T H2 ), and V H3 (T H3 ) of the heater element 61A when the temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and the voltage V I of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (45), below.
  • C 0 h 5 V H ⁇ 1 T H ⁇ 1 , V H ⁇ 2 T H ⁇ 2 , V H ⁇ 3 T H ⁇ 3 , V I
  • the concentration of caloric component C 0 of a mixed gas can also be obtained as an equation having, as variables, the output voltages AD H1 (T H1 ), AD H2 (T H2 ), and AD H3 (T H3 ) of analog-digital converting circuits that are connected to the heater element 61 A when the temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and the output voltage AD I of an A/D converting circuit that is connected to the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (46), below.
  • C 0 h 6 AD H ⁇ 1 T H ⁇ 1 , AD H ⁇ 2 T H ⁇ 2 , AD H ⁇ 3 T H ⁇ 3 , AD I
  • the concentration of caloric component C 0 of a mixed gas can also be obtained from an equation having, as variables, electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61A when the heat producing temperatures of the heater element 61 A are T H1 , T H2, and T H3 , and an electric signal S I from the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (47), below.
  • C 0 h 7 S H ⁇ 1 T H ⁇ 1 , S H ⁇ 2 T H ⁇ 2 , S H ⁇ 3 T H ⁇ 3 , S I
  • the measuring portion 321 measures the value of the electric signal S I from the first temperature measuring element 62A, and, from the heater element 61 A, the values of the electric signal S H1 (T H1 ) at the heat producing temperature T H1 , the electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and the electric signal S H3 (T H3 ) at the heat producing temperature T H3 , and stores the measured values in the electric signal storing device 421.
  • the concentration of caloric component calculating equation generating portion 352 uses multivariate analysis based on the collected values for the caloric component densities C 0 , the electric signals S I , and the electric signals S H , to generate a concentration of caloric component calculating equation having the electric signal S, from the: first temperature measuring element 62A and the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61 A as the independent variables, and the concentration of caloric component C 0 as the dependent variable.
  • the other structural elements of the concentration of caloric component calculating equation generating system 22B illustrated in FIG. 23 are identical to those of the concentration of caloric component calculating equation generating system 22A that is illustrated in FIG. 16 , so explanations thereof are omitted.
  • a concentration of caloric component measuring system 23B as set forth below includes a measuring portion 321 for measuring the value of an electric signal S I from the first temperature measuring element 62A, which is dependent on the temperature T I of the gas being measured, and values of the electric signals S H from the heater element 61A at each of the plurality of heat producing temperatures T H ; a density calculating equation storing device 452 for storing a concentration of caloric component calculating equation that has the electric signal S I from the first temperature measuring element 62A and the electric signals S H from the heater element 61 A at the plurality of heat producing temperatures T H as independent variables and the concentration of caloric component C 0 as the dependent variable; and a density calculating portion 355 for calculating the value of the concentration of caloric component C 0 of the mixed gas being measured, by substituting the measured value of the electric signal S I from the first temperature measuring element 62A and the measured values of the electric signals S H from the heater element 61 A into the independent variable that is the electric
  • the concentration of caloric component calculating equation includes, for example, as independent variables, the electric signal S I from the first temperature measuring element 62A, the electric signal S H1 (T H1 ) from the heater element 61A at a heat producing temperature T H1 of 100°C, the electric signal S H2 (T H2 ) from the heater element 61A at a heat producing temperature T H2 of 150°C, and the electric signal S H3 (T H3 ) from the heater element 61 A at a heat producing temperature T H3 of 200°C.
  • the heater element 61A that is in contact with the mixed gas being measured produces heat at a temperature T H1 of 100°C, a temperature T H2 of 150°C, and a temperature T H3 of 200°C, for example, to output an electric signal S H1 (T H1 ) at the heat producing temperature T H1 , an electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and an electric signal S H3 (T H3 ) at the heat producing temperature T H3 .
  • the measuring portion 321 measures the value of the electric signal S I from the first temperature measuring element 62A, which is in contact with the mixed gas being measured, and, from the heater element 61A, which is in contact with the mixed gas being measured, the values of the electric signal S H1 (T H1 ) at the heat producing temperature T H1 , the electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and the electric signal S H3 (T H3 ) at the heat producing temperature T H3 , and stores the measured values in the electric signal storing device 421.
  • the density calculating portion 355 substitutes the respected respective measured values into the independent variables of the electric signal S 1 from the first temperature measuring element 62A and the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 , (T H3 ) from the heater element 61A in the concentration of caloric component calculating equation that is stored in the density calculating equation storing device 452, to calculate the value of the concentration of caloric component C 0 of the mixed gas being measured.
  • the other structural elements of the concentration of caloric component measuring system 23B illustrated in FIG. 24 are identical to those of the concentration of caloric component measuring system 23A that is illustrated in FIG. 18 , so explanations thereof are omitted.
  • Equation (48), below from an equation having, as variables, the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas, and the temperature T I of the mixed gas, when the heat producing temperatures of the heater element 61A are T H1 , T H2 , and T H3 .
  • Cp / k g 7 M I T H ⁇ 1 , M I T H ⁇ 2 , M I T H ⁇ 3 , T I
  • the specific heat capacity Cp divided by the thermal conductivity k in the mixed gas being measured can be obtained uniquely by measuring the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas when the heat producing temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and then substituting into Equation (48).
  • Equation (23) if the mixed gas includes an alkane (C j H 2j +2) other than methane (CH4) and propane (C 3 H 8 ), where j is a natural number, in addition to methane (CH 4 ) and propane (C 3 H 8 ), then the alkane (C j H 2j+2 ) other than methane (CH 4 ) and propane (C 3 H 8 ) will be seen as a mixture of methane (CH 4 ) and propane (C 3 H 8 ), so there will be no effect on the calculation in Equation (49). Also, if the temperature T 1 of the mixed gas previous to the heater element 61 A, illustrated in FIG. 1 and FIG. 2 , being caused to produce heat is stable, then Equation (49) need not include the variable for the temperature T I of the mixed gas.
  • the specific heat capacity calculating equation generating system 24A comprises a chamber 101 that is filled with sample mixed gases for which the specif heat capacities Cp divided by the thermal conductivities k are known in advance, and a measuring mechanism 10 for measuring the values of a plurality of radiation coefficients M I of the sample mixed gases and the values of the temperatures T I of the sample mixed gases.
  • the specific heat capacity calculating equation generating system 24A comprises a specific heat capacity calculating equation generating portion 362 for generating a specific heat capacity calculating equation using the radiation coefficients M I and the gas temperatures T I for a plurality of heat producing temperatures of the heater element 61 A as independent variables and the specific heat capacity Cp divided by the thermal conductivity k in the gas as the dependent variable, based on the values of the specific heat capacities Cp divided by the thermal conductivities k in a plurality of sample mixed gases, a plurality of measured values for the plurality of radiation coefficients M I of the sample mixed gases, and a plurality of measured values for the temperatures T I of the sample mixed gases.
  • the measuring mechanism 10 and heat dissipation factor storing device 401 are the same as above, so the explanations thereof are omitted.
  • the specific heat capacity calculating equation generating portion 362 collects the respective known specific heat capacities Cp divided by the thermal conductivities k in the first through fourth sample mixed gases, for example, the plurality of measured values for the radiation coefficients M I for the gas when the heat producing temperature of the heater element 61 A was 100°C, the plurality of measured values for the radiation coefficients M I for the gas when the heat producing temperature of the heater element 61A was 150°C, and the plurality of measured values for the gas the radiation coefficients M I for when the heat producing temperature of the heater element 61A was 200°C.
  • the specific heat capacity calculating equation generating portion 362 calculates a specific heat capacity calculating equation having, as independent variables, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 100°C, the radiation coefficient M I when the heat producing temperature of the heater element 61 A is 150°C, the radiation coefficient M I when the heat producing temperature of the heater element 61A is 200°C, and the gas temperature T I , and having, as the dependent variable, the specific heat capacity Cp divided by the thermal conductivity k.
  • the specific heat capacity calculating equation generating system 24A is further provided with a specific heat capacity calculating equation storing device 462, connected to the CPU 300.
  • the specific heat capacity calculating equation storing device 462 stores the specific heat capacity calculating equation generated by the specific heat capacity calculating equation generating portion 362.
  • the flowchart in FIG. 26 is used next to explain a method for generating a specific heat capacity calculating equation. Note that in the example below a case is explained wherein the first through fourth sample mixed gases are prepared and the heater element 61A of the microchip 8A illustrated in FIG. 25 is caused to produce heat at 100°C, 150°C, and 200°C.
  • the method for generating a specific heat capacity calculating equation enables the generation of a specific heat capacity calculating equation that calculates a unique value for the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas being measure.
  • a specific heat capacity measuring system 25A according to FIG. 27 includes a chamber 101 that is filled with a mixed gas to be measured for which the specific heat capacity Cp divided by the thermal conductivity k is unknown, and a measuring mechanism 10 for measuring the value of the temperature T I of the mixed gas to be measured and the values of a plurality of radiation coefficients M I of the mixed gas to be measured.
  • the specific heat capacity measuring system 25A further has a specific heat capacity calculating equation storing device 462 for storing a specific heat capacity calculating equation having, as independent variables, the temperature T I of the gas and the radiation coefficients M I for the gas at a plurality of heat producing temperatures of the heater element 61A, and having, as the independent variable, the specific heat capacity Cp divided by the thermal conductivity k; and a specific heat capacity calculating portion 365 for calculating the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured, by substituting the value for the temperature T I of the mixed gas being measured and the radiation coefficients M I , for the mixed gas being measured, at a plurality of heat producing temperatures of the heater element 61 A into the independent variables of the temperature T I of the gas and the radiation coefficients M I for the gas at a plurality of heat producing temperatures of the heater element 61 A in the specific heat capacity calculating equation.
  • the specific heat capacity calculating equation storing device 462 stores the specific heat capacity calculating equation.
  • natural gases including methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 )
  • CH 4 methane
  • propane C 3 H 8
  • nitrogen N 2
  • CO 2 carbon dioxide
  • the specific heat capacity calculating equation uses, as independent variables, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61 A is 100°C, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 150°C, the radiation coefficient M I of the gas when the heat producing temperature of the heater element 61A is 200°C, and the temperature T I of the gas.
  • a natural gas that includes, in unknown volume fractions, methane (CH 4 ), propane (C 3 H 8 ), nitrogen (N 2 ), and carbon dioxide (CO 2 ), and for which the value of the specific heat capacity Cp divided by the thermal conductivity k is unknown, is introduced into the chamber 101 as the mixed gas to be measured.
  • the measuring mechanism 10 and heat dissipation factor storing device 401 are the same as above so the explanations thereof are omitted.
  • the specific heat capacity calculating portion 365 substitutes the values of the radiation coefficients M I and the temperature T I of the mixed gas being measured into the independent variables of the radiation coefficients M I for the gas and the temperature T I of the gas in the specific heat capacity calculating equation, to calculate the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured.
  • a specific heat capacity storing device 463 is also connected to the CPU 300. The specific heat capacity storing device 463 stores the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured, calculated by the specific heat pass the calculating portion 365.
  • the requirements for the other structural elements in the specific heat capacity measuring system 25A are identical to those in the specific heat capacity calculating equation generating system 24A set forth above, so explanations thereof are omitted.
  • the flowchart in FIG. 28 is used next to explain a method for measuring a specific heat capacity. Note that in the example below a case is explained the heater element 61 A of the microchip 8A illustrated in FIG. 27 is caused to produce heat at 100°C, 150°C, and 200°C.
  • Step S204 the specific heat capacity calculating portion 365 substitutes the value of the temperature T I of the mixed gas being measured into the independent variable of the temperature T I in the specific heat capacity calculating equation, and substitutes the value of the radiation coefficients M I of the mixed gas being measured into the independent variable of the radiation coefficients M I in the specific heat capacity calculating equation, to calculate the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured.
  • the specific heat capacity calculating portion 365 stores, into the specific heat capacity storing device 463, the value calculated for the specific heat capacity Cp divided by the thermal conductivity k, to complete the method for measuring the specific heat capacity.
  • the method for measuring the specific heat capacity described above enables the measurement of the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas that is a mixed gas to be measured, from measured values for the radiation coefficients M I of the mixed gas to be measured, without using costly gas chromatography equipment or speed-of-sound sensors.
  • the equation for calculating the specific heat capacity Cp divided by the thermal conductivity k was used to calculate calculated values for the specific heat capacities Cp divided by the thermal conductivities k in the 19 sample mixed gases, and the true values for the specific heat capacities Cp divided by the thermal conductivities k in the 19 sample mixed gases were compared.
  • the error in the calculated values, relative to the true values for the specific heat capacities Cp divided by the thermal conductivities k as illustrated in FIG. 29 and FIG. 30 , where within -0.6% and +0.6%.
  • the specific heat capacity Cp divided by the thermal conductivity k in the mixed gas that has the four types of gas components is obtained as an equation having, as variables, the radiation coefficients M I (T H1 ), M I (T H2 ), and M I (T H3 ) of the mixed gas when the heat producing temperatures of the heater element 61A are T H1 , T H2 , and T H3 .
  • the radiation coefficient M I of the mixed gas depends on the resistance value R H of the heater element 61A and on the resistance value R I of the first temperature measuring element 62A.
  • the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained as an equation having, as variables, the resistances R H1 (T H1 ), R H2 (T H2 ), and R H3 (T H3 ) of the heater element 61A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the resistance value R I of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (50), below.
  • Cp / k g 8 R HI T H ⁇ 1 , R H ⁇ 2 T H ⁇ 2 , R H ⁇ 3 T H ⁇ 3 , R I
  • the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can be calculated uniquely by measuring the resistances R H1 (T H1 ), R H2 (T H2 ), and R H3 (T H3 ) of the heater element 61A when the heat producing temperatures of the heater element 61 A, which is in contact with the mixed gas, are T H1 , T H2 , and T H3 , and the resistance value R I of the first temperature measuring element 62A that is in contact with the mixed gas prior to the heat production by the heater element 61 A, for example, and then substituting into Equation (50).
  • the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained as an equation having, as variables, the currents I H1 (T H1 ), I H2 (T H2 ), and I H3 (T H3 ) flowing in the heater element 61A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the current I I flowing in the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (51), below.
  • Cp / k g 9 I HI T H ⁇ 1 , I H ⁇ 2 T H ⁇ 2 , I H ⁇ 3 T H ⁇ 3 , I I I
  • the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained from an equation having, as variables, the voltages V H1 (T H1 ), V H2 (T H2 ), and V H3 (T H3 ) of the heater element 61A when the temperatures of the heater element 61A are T H1 , T H2, and T H3 , and the voltage V I of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (52), below.
  • Cp / k g 10 V HI T H ⁇ 1 , V H ⁇ 2 T H ⁇ 2 , V H ⁇ 3 T H ⁇ 3 , V I
  • the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained as an equation having, as variables, the output voltages AD H1 (T H1 ), AD H2 (T H2 ), and AD H3 (T H3 ) of analog-digital converting circuits that are connected to the heater element 61A when the temperatures of the heater element 61A are T H1 , T H2 , and T H3 , and the output voltage AD I of an A/D converting circuit that is connected to the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (53), below.
  • Cp / k g 11 AD HI T H ⁇ 1 , AD H ⁇ 2 T H ⁇ 2 , AD H ⁇ 3 T H ⁇ 3 , AD I
  • Cp divided by the thermal conductivity k in a mixed gas can also be obtained from an equation having, as variables, electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61 A when the heat producing temperatures of the heater element 61 A are T H1 , T H2 , and T H3 , and an electric signal S I from the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (54), below.
  • Cp / k g 12 S HI T H ⁇ 1 , S H ⁇ 2 T H ⁇ 2 , S H ⁇ 3 T H ⁇ 3 , S I
  • a specific heat capacity calculating equation generating system 24B as illustrated in FIG. 31 includes a measuring portion 321, illustrated in FIG. 31 , for measuring values of electric signals S I from the first temperature measuring element 62A, illustrated in FIG. 1 and FIG. 2 , that are dependent on the respective temperatures T I of the plurality of sample mixed gases, and the values of electric signals S H from the heater element 61 A at each of the plurality of heat producing temperatures T H ; and a specific heat capacity calculating equation generating portion 362 for generating a specific heat capacity calculating equation based on known values for specific heat capacities Cp divided by thermal conductivities k in a plurality of sample mixed gases, the measured value for the electric signal S I from the first temperature measuring element 62A, and the plurality of measured values for the electric signals from the heater element 61 A at the plurality of heat producing temperatures, having an electric signal S I from the first temperature measuring element 62A and the electric signals S H from the heater element 61A at the plurality of heat producing temperatures T H as independent variables, and having the
  • the measuring portion 321 measures the value of the electric signal S I from the first temperature measuring element 62A, and, from the heater element 61A, the values of the electric signal S H1 (T H1 ) at the heat producing temperature T H1 , the electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and the electric signal S H3 (T H3 ) at the heat producing temperature T H3 , and stores the measured values in the electric signal storing device 421.
  • the specific heat capacity calculating equation generating portion 362 that is included in the CPU 300 collection the respective known values for the specific heat capacities Cp divided by the thermal conductivities k in, for example, each of the first through fourth sample mixed gases, the plurality of measured values for the electric signals S I from the first temperature measuring element 62A, and the plurality of measured values for the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61A.
  • the specific heat capacity calculating equation generating portion 362 uses multivariate analysis based on the collected values for the specific heat capacities Cp divided by the thermal conductivities k, the electric signals S I , and the electric signals S H , to generate a specific heat capacity calculating equation having the electric signal S I from the first temperature measuring element 62A and the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61A as the independent variables, and the specific heat capacity Cp divided by the thermal conductivity k in as the dependent variable.
  • the other structural elements of the specific heat capacity calculating equation generating system 24B illustrated in FIG. 31 are identical to those of the specific heat capacity calculating equation generating system 24A that is illustrated in FIG. 25 , so explanations thereof are omitted.
  • a specific heat capacity measuring system 25B as set forth has a measuring portion 321 for measuring the value of an electric signal S I from the first temperature measuring element 62A, which is dependent on the temperature T I of the gas being measured, and values of the electric signals S H from the heater element 61A at each of the plurality of heat producing temperatures T H ; a specific heat capacity calculating equation storing device 462 for storing a specific heat capacity calculating equation that has the electric signal S I from the first temperature measuring element 62A and the electric signals S H from the heater element 61 A at the plurality of heat producing temperatures T H as independent variables and the specific heat capacity Cp divided by the thermal conductivity k as the dependent variable; and a specific heat capacity calculating portion 365 for calculating the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured, by substituting the measured value of the electric signal S I from the first temperature measuring element 62A and the measured values of the electric signals S H from the heater element 61A into the independent
  • the specific heat capacity calculating equation includes, for example, as independent variables, the electric signal S I from the first temperature measuring element 62A, the electric signal S H1 (T H1 ) from the heater element 61A at a heat producing temperature T H1 of 100°C, the electric signal S H2 (T H2 ) from the heater element 61A at a heat producing temperature T H2 of 150°C, and the electric signal S H3 (T H3 ) from the heater element 61A at a heat producing temperature T H3 of 200°C.
  • the first temperature measuring element 62A of the microchip 8A illustrated in FIG. 1 and FIG. 2 outputs an electric signal S I that is dependent on the temperature of the gas that is measured.
  • the heater element 61 A applies driving powers P H1 , P H2 , and P H3 from the driving circuit 303 illustrated in FIG. 32 .
  • the heater element 61 A that is in contact with the mixed gas being measured produces heat at a temperature T H1 of 100°C, a temperature T H2 of 150°C, and a temperature T H3 of 200°C, for example, to output an electric signal S H1 (T H1 ) at the heat producing temperature T H1, an electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and an electric signal S H3 (T H3 ) at the heat producing temperature T H3 .
  • the measuring portion 321 measures the value of the electric signal S I from the first temperature measuring element 62A, which is in contact with the mixed gas being measured, and, from the heater element 61A, which is in contact with the mixed gas being measured, the values of the electric signal S H1 (T H1 ) at the heat producing temperature T H1 , the electric signal S H2 (T H2 ) at the heat producing temperature T H2 , and the electric signal S H3 (T H3 ) at the heat producing temperature T H3 , and stores the measured values in the electric signal storing device 421.
  • the specific heat capacity calculating portion 365 substitutes the respected respective measured values into the independent variables of the electric signal S I from the first temperature measuring element 62A and the electric signals S H1 (T H1 ), S H2 (T H2 ), and S H3 (T H3 ) from the heater element 61 A in the specific heat capacity calculating equation that is stored in the specific heat capacity calculating equation storing device 462, to calculate the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured.
  • the other structural elements of the specific heat capacity measuring system 25B illustrated in FIG. 32 are identical to those of the specific heat capacity measuring system 25A that is illustrated in FIG. 27 , so explanations thereof are omitted.
  • the flow rate measuring system includes a thermal diffusivity measuring system 21 A; and a flow meter 41 A for measuring a flow rate Q of the mixed gas being measured, for which the thermal diffusivity was measured by the thermal diffusivity measuring system 21A.
  • the thermal diffusivity measuring system 21A and the flow meter 41 A are connected by a flow path 103 wherein flows the mixed gas being measured.
  • the thermal diffusivity measuring system 21A was explained above, and thus the description thereof will be omitted.
  • the thermal diffusivity measuring system 21 A and the flow meter 41 A are connected electrically by an interconnection 201.
  • the flow meter 41 A as illustrated in FIG. 34 , which is a cross-sectional diagram, has a flow path holding unit 15 that is provided with a flow path 11 wherein flows the mixed gas being measured, and a controlling unit 30, disposed on the flow path holding unit 15.
  • the controlling unit 30 comprises a CPU 330. Note that while FIG. 34 is a cross-sectional diagram, the interior of the controlling unit 30 is drawn schematically, and actually a microprocessor, a random access memory (RAM), a read-only memory (ROM), I/O circuitry, and the like, are disposed within the controlling unit 30.
  • a filling opening 13 and a discharge opening 14 are provided in the flow path holding unit 15, and a flow path 11 passes through the interior of the flow path holding unit 15 from the filling opening 13 to the discharge opening 14.
  • a flow path 103, illustrated in FIG. 33 passes through the filling opening 13.
  • the microchip 8B is disposed on an inner wall of the flow path 11.
  • the microchip 8B as illustrated in FIG. 35 , which is a perspective view, and in FIG. 36 , which is a cross-sectional diagram unit from the direction of section XXXVI-XXXVI, has a structure that is identical to that of the microchip 8A that was explained above.
  • the microchip 8B has a substrate 60B, which is provided with a cavity 66B, a dielectric layer 65B, which is disposed so as to cover the cavity 66B on the substrate 60B, and a heater 61 B that is disposed on the dielectric layer 65B.
  • the microchip 8B comprises an upstream temperature measuring resistive element 62B, illustrated in FIG.
  • the portion of the dielectric layer 65B that covers the cavity 66B forms a thermally insulating diaphragm.
  • the peripheral temperature sensor 64B measures the temperature of the mixed gas being measured that has flowed into the flow path 11, illustrated in FIG. 34 .
  • the heater 61B illustrated in FIG. 35 and 36 , is disposed in the center of the dielectric layer 65B that covers the cavity 66B, and heats the mixed gas being measured, which flows in the flow path 11, so as to be constant temperature higher, such as, for example, 10°C higher, than the temperature measured by the peripheral temperature sensor 64B.
  • the upstream temperature measuring resistive element 62B is used to detect the temperature on the upstream side of the heater 61B
  • the downstream temperature measuring resistive element 63B is used to detect the temperature on the downstream side of the heater 61B.
  • the heat that is added by the heater 61B, illustrated in FIG. 35 and FIG. 36 diffuses symmetrically to the upstream side and the downstream side. Consequently, the temperatures of the upstream temperature measuring resistive element 62B and the downstream temperature measuring resistive element 63B are be equal, and thus the electrical resistance of the upstream temperature measuring resistive element 62B and the downstream temperature measuring resistive element 63B are equal.
  • the flow rate Q of the mixed gas flowing within the flow path 11 illustrated in FIG. 34 is calculated from the difference between the electrical resistance of the downstream temperature measuring resistive element 63B, illustrated in FIG. 35 and FIG. 36 , and the electrical resistance of the upstream temperature measuring resistive element 62B.
  • the units for the flow rate Q are, for example, m 3 /s or m 3 /h.
  • An orifice 12 for narrowing the inner diameter of the flow path 11 is provided in a portion of the flow path 11.
  • the cross-sectional area of the flow path 11 in the orifice 12 is set appropriately to cause the speed of flow of the mixed gas that is being measured in the flow path 11 to be within the measurement range of the microchip 8B.
  • the microchip 8B is connected electrically to the CPU 330 of the controlling unit 30.
  • the flow rate calculating portion 331 of the CPU 330 receives, from the microchip 8B, the value of the electrical resistance of the downstream temperature measuring resistive element 63B, illustrated in FIG. 35 and FIG. 36 , and the value of the electrical resistance of the upstream temperature measuring resistive element 62B. Furthermore, the flow rate calculating portion 331, illustrated in FIG. 34 , calculates the value of the flow rate Q of the mixed gas being measured, which flows in the flow path 11, illustrated in FIG. 34 , based on the difference between the value of the electrical resistance of the downstream temperature measuring resistive element 63B, illustrated in FIG. 35 and FIG. 36 , and the value of the electrical resistance of the upstream temperature measuring resistive element 62B.
  • the flow rate Q of the gas tends to have error that increases with the inverse 1/ ⁇ of the thermal diffusivity of the gas.
  • the flow rate sensor was first calibrated using, as the calibration gas, a public utility gas 13A wherein the calorific value was adjusted to 45 MJ/m 3 .
  • the first through sixth mixed gases having the components presented in FIG. 37 were prepared.
  • the first through sixth mixed gases, as illustrated in FIG. 38 had different inverse 1/ ⁇ thermal diffusivities.
  • error occurred proportional to the inverse 1/ ⁇ thermal diffusivities.
  • the correcting portion 332 receives the detected value for the flow rate Q of the mixed gas being measured, calculated by the flow rate calculating portion 331. Moreover, the correcting portion 332 receives the measured value for the inverse 1/ ⁇ 1 of the thermal diffusivity of the mixed gas being measured, from the thermal diffusivity measuring system 21 A, through the interconnection 201 illustrated in FIG. 33 .
  • the correcting portion 332, illustrated in FIG. 34 divides the detected value for the flow rate Q for the mixed gas being measured by the inverse 1/ ⁇ 0 of the thermal diffusivity of the calibration gas and then multiplies by the inverse 1/ ⁇ 1 of the thermal diffusivity of the mixed gas being measured, as shown by Equation (55), below.
  • the flow rate measuring system as set forth and illustrated in FIG. 40 has a thermal diffusivity measuring system 21B; and a flow meter 41 A for measuring a flow rate Q of the mixed gas being measured, for which the thermal diffusivity was measured by the thermal diffusivity measuring system 21B.
  • the thermal diffusivity measuring system 21B is identical to that above. Additionally, because, in the flow meter 41 A, the method for correcting the detected value for the flow rate Q of the mixed gas being measured using the measured value of the inverse 1/ ⁇ of the thermal diffusivity of the mixed gas being measured, measured by the thermal diffusivity measuring system 21B, is identical to that above as well, the explanation thereof will be omitted.
  • a flow rate measuring system as illustrated in FIG. 41 has a specific heat capacity measuring system 25A; and a flow meter 41C for measuring a flow rate Q of the mixed gas being measured, for which the specific heat capacity Cp divided by the thermal conductivity k was measured by the specific heat capacity measuring system 25A.
  • the specific heat capacity measuring system 25A and the flow meter 41C are connected by a flow path 103 wherein flows the mixed gas being measured.
  • the specific heat capacity measuring system 25A was explained above, and thus the description thereof will be omitted.
  • the specific heat capacity measuring system 25A and the flow meter 41C are connected electrically by an interconnection 201.
  • the CPU 330 of the flow meter 41C is provided with a mass flow rate calculating portion 334 for calculating the mass flow rate Qm of the mixed gas being measured, based on the detected value for the volumetric flow rate Q of the mixed gas being measured and the measured value for the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured.
  • the mass flow rate calculating portion 334 receives the detected value for the volumetric flow rate Q of the mixed gas being measured, calculated by the flow rate calculating portion 331.
  • the mass flow rate calculating portion 334 receives the measured value for the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured, from the specific heat capacity measuring system 25A, through the interconnection 201 illustrated in FIG. 41 .
  • Equation (56) the detected value for the volumetric flow rate Q of the mixed gas being measured, calculated by the flow rate calculating portion 331, as shown by Equation (56), below, is proportional to the product of the thermal diffusivity ⁇ and the flow speed d.
  • A is a constant.
  • the mass flow rate calculating portion 334 obtains the product of the density ⁇ and the flow speed d by dividing the detected value for the volumetric flow rate Q of the mixed gas being measured by the specific heat capacity Cp divided by the thermal conductivity k, and by the constant A, as shown in Equation (57), below.
  • Q / A Cp / k ⁇ x d
  • the mass flow rate calculating portion 334 calculates the mass flow rate Qm of the mixed gas being measured by multiplying the product of the density ⁇ and the flow speed d, thus obtained, by the cross-sectional area u of the orifice 12.
  • the units for the mass flow rate Qm are, for example, kg/s or kg/h.
  • Qm ⁇ x d x u
  • the other structural elements of the flow meter 41C are identical to those of the flow meter 41 A that is illustrated in FIG. 34 , so explanations thereof are omitted.
  • a flow rate measuring system as illustrated in FIG. 43 has a specific heat capacity measuring system 25B; and a flow meter 41C for measuring a flow rate Q of the mixed gas being measured, for which the specific heat capacity Cp divided by the thermal conductivity k was measured by the specific heat capacity measuring system 25B.
  • the specific heat capacity measuring system 25B is identical to that above.
  • the method for calculating the mass flow rate Qm is the same as other examples above, so the explanation thereof is omitted.
  • the flow rate measuring system as set forth and illustrated in FIG. 44 , includes a concentration of caloric component measuring system 23A; and a flow meter 41B for measuring a flow rate Q of the mixed gas being measured, for which the concentration of caloric component C 0 was measured by the concentration of caloric component measuring system 23A.
  • the concentration of caloric component measuring system 23A and the flow meter 41 B are connected by a flow path 103 wherein flows the mixed gas being measured.
  • the concentration of caloric component measuring system 23A was explained, and thus the description thereof will be omitted.
  • the concentration of caloric component measuring system 23A and the flow meter 41 B are connected electrically by an interconnection 201.
  • the CPU 330 of the flow meter 41B is provided with a calorific flow rate calculating portion 333 for calculating the calorific flow rate Qc of the caloric components of the mixed gas being measured, based on the detected value for the flow rate Q of the mixed gas being measured and the measured value for the concentration of caloric component C 0 of the mixed gas being measured.
  • the calorific flow rate calculating portion 333 receives the value for the mass flow rate Qm of the mixed gas being measured, calculated by the mass flow rate calculating portion 334.
  • the calorific flow rate calculating portion 333 receives the measured value for the concentration of caloric component of the mixed gas being measured, from the concentration of caloric component measuring system 23A, through the interconnection 201 illustrated in FIG. 44 .
  • the calorific flow rate calculating portion 333 calculates the flow rate Q C of the caloric component within the mixed gas being measured, as shown in Equation (59), below, by multiplying the concentration of caloric component C 0 of the mixed gas being measured by the mass flow rate Qm of the mixed gas being measured.
  • Q C Qm x C O
  • the flow rate measuring system enables the accurate measurement of the flow rate of the caloric components of the mixed gas being measured.
  • the other structural elements of the flow meter 41B are identical to those of the flow meter 41A that is illustrated in FIG. 34 , so explanations thereof are omitted.
  • the flow rate measuring system of an embodiment of the invention has a concentration of caloric component measuring system 23B; and a flow meter 41B for measuring a flow rate Q of the mixed gas being measured, for which the concentration of caloric component C 0 was measured by the concentration of caloric component measuring system 23B.
  • the concentration of caloric component measuring system 23B is identical to that above. Additionally, because, in the flow meter 41 B, the method for calculating the flow rate Q C of the caloric component of the mixed gas being measured using the detected values for the concentration of caloric component C 0 and for the flow rate Q of the mixed gas being measured is identical to that in other examples, the explanation thereof will be omitted.
  • FIG. 47 shows the relationship between the radiation coefficient and the thermal conductivity in a mixed gas when electric currents of 2 mA, 2.5 mA, and 3 mA are applied to the heat producing resistor. As illustrated in FIG. 47 , typically there is a proportional relationship between the radiation coefficient and the thermal conductivity of the mixed gas.
  • the generation of the calorific value calculating equation and the calculation of the calorific value may be performed using the thermal conductivities at a plurality of measurement temperatures of the mixed gasse.

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Claims (2)

  1. Système de mesure de débit, comprenant :
    - un mécanisme de mesure (10) conçu pour mesurer au moins l'un d'un coefficient de rayonnement ou d'une valeur pour une conductivité thermique pour un mélange de gaz mesuré,
    - un capteur de débit conçu pour détecter un débit du mélange de gaz mesuré, étalonné en utilisant un gaz d'étalonnage, et
    - une partie de correction (332) conçue pour corriger une erreur de détection du débit,
    caractérisé :
    - en ce que ledit mécanisme de mesure (10) est conçu pour mesurer au moins l'un d'un coefficient de rayonnement ou d'une valeur pour une conductivité thermique pour un mélange de gaz mesuré lorsqu'un élément de dispositif de chauffage (61 A) a produit de la chaleur à une pluralité de températures de production de chaleur ;
    - par un dispositif de mémorisation d'équation de calcul de diffusivité thermique (402) mémorisant une équation de calcul de diffusivité thermique qui utilise au moins l'un des coefficients de rayonnement ou des conductivités thermiques pour la pluralité de températures de production de chaleur en tant que variables indépendantes et qui utilise une diffusivité thermique en tant que variable dépendante ;
    - par une partie de calcul de diffusivité thermique (305) conçue pour calculer une valeur pour l'inverse 1/α de la diffusivité thermique du mélange de gaz mesuré par la substitution des valeurs d'au moins l'un des coefficients de rayonnement (M1) ou des conductivités thermiques du mélange de gaz mesuré pour la pluralité de températures de production de chaleur (TH1, TH2, TH3, THn-1), aux variables indépendantes d'au moins l'un des coefficients de rayonnement ou des conductivités thermiques, pour la pluralité de températures de production de chaleur, dans l'équation de calcul de diffusivité thermique ;
    - en ce que le capteur de débit comprend une micropuce (8B) qui comprend un dispositif de chauffage (61 B) et un élément de mesure de température (63B) ; et
    - en ce que ladite partie de correction (332) est conçue pour corriger une erreur de détection de débit due à une différence entre la valeur pour l'inverse de la diffusivité thermique du gaz d'étalonnage et la valeur pour l'inverse de la diffusivité thermique du mélange de gaz mesuré.
  2. Système de mesure de débit selon la revendication 1, dans lequel :
    la partie de correction (332) est conçue pour corriger l'erreur de détection du débit mesuré par le capteur de débit sur la base d'un rapport entre la valeur pour l'inverse de la diffusivité thermique du gaz d'étalonnage et la valeur pour l'inverse de la diffusivité thermique du mélange de gaz mesuré.
EP11163139.6A 2010-04-20 2011-04-20 Système de mesure du débit de fluide avec correction pour la diffusion thermique Not-in-force EP2381248B1 (fr)

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JP5534193B2 (ja) 2014-06-25
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